In the past few decades, the petroleum industry has invested heavily in the development of marine seismic survey techniques that yield knowledge of subterranean formations beneath a body of water in order to find and extract valuable mineral resources, such as oil. High-resolution seismic images of a subterranean formation are essential for quantitative seismic interpretation and improved reservoir monitoring. For a typical marine seismic survey, an exploration-seismology vessel tows one or more seismic sources and one or more streamers that form a seismic data acquisition surface below the surface of the water and over a subterranean formation to be surveyed for mineral deposits. The vessel contains seismic acquisition equipment, such as navigation control, seismic source control, seismic receiver control, and recording equipment. The seismic source control causes the one or more seismic sources, which are typically air guns, to produce acoustic impulses at selected times. Each impulse is a sound wave that travels down through the water and into the subterranean formation. At each interface between different types of rock, a portion of the sound wave is refracted, a portion of the sound wave is transmitted, and another portion is reflected back toward the body of water to propagate up toward the water surface. The streamers towed behind the vessel are elongated cable-like structures. Each streamer includes a number of seismic receivers or sensors that detect pressure and/or velocity wavefields associated with the sound waves reflected back into the water from the subterranean formation.
Sound waves that propagate down into the subsurface and undergo a single reflection from an interface before being detected by seismic receivers are called “primary reflections,” and sound waves that take several subsurface reflections before being detected by seismic receivers are called “multiple reflections.” Multiple reflections may also be primary reflections that are subsequently reflected from the sea surface down into the subsurface before being detected by the receivers. In the past, conventional imaging techniques relied almost exclusively on the primary reflections. As a result, significant computational effort was dedicated to attenuating the multiple reflections. In recent years, however, the multiple reflections have been recognized as providing additional, valuable information about the subterranean formation. In particular, multiple reflections that include at least one reflection from the sea-surface, called “sea-surface multiples,” are typically the strongest and most significant of the multiple reflections to use in imaging a subterranean formation. When a subterranean formation is imaged with wavefields associated with the primary and multiple reflections, the direct incident wavefield that originates from the source is significant for using the primary reflections in the imaging process. However, due to the large minimal lateral distance between the source and the nearest receivers and the large distance between streamers of a typical acquisition system, measurement of the direct incident wavefield is difficult. As a result, those working in the petroleum industry continue to seek systems and methods that can be used to measure the direct incident wavefield.